Doubly truncated survival data arise if failure times are observed only within certain time intervals. The nonparametric maximum likelihood estimator is widely used to estimate the underlying failure time distribution. Using a directed graph representation of the data suggested by Vardi (1985), a certain graphical condition holds if and only if the nonparametric maximum likelihood estimate exists and is unique. If this condition does not hold, then such an estimate may exist but need not be unique, so another graphical condition is proposed to check whether such an estimate exists. The conditions are simple to check using existing graphical software. Reanalysis of an AIDS incubation time dataset shows that a nonparametric maximum likelihood estimate does not exist for these data.

中文翻译：

---

带双截断的非参数最大似然估计

如果仅在特定时间间隔内观察到故障时间，则会出现双重截断的生存数据。非参数最大似然估计器被广泛用于估计潜在的故障时间分布。使用 Vardi (1985) 建议的数据的有向图表示，当且仅当非参数最大似然估计存在且唯一时，某个图形条件成立。如果这个条件不成立，那么这样的估计可能存在但不必是唯一的，所以提出另一个图形条件来检查这样的估计是否存在。使用现有的图形软件很容易检查这些条件。对 AIDS 潜伏时间数据集的重新分析表明，这些数据不存在非参数最大似然估计。